Grimm (2018) — Grammatical Number and the Scale of Individuation #

Formalizes the core framework of:

Grimm, S. (2018). Grammatical number and the scale of individuation. Language 94(3). 527–574.

Core contributions #

The scale of individuation (his (17)/(19)): individuation types — equivalence classes of nominal descriptions by individuation properties — are linearly ordered: substance < granular aggregate < collective aggregate < individual.
The order-preservation thesis (his §3.4): a language's grammatical countability classes also partition nominal descriptions, and the classification map from individuation types to countability classes is order-preserving. Consequently every countability class is a contiguous segment of the scale — formally, the fibers of a monotone classification are Set.OrdConnected (the same mathlib predicate that states [Har14a]'s convexity condition in Syntax/Minimalist/Phi/Recursion.lean). His hypothetical discontinuous system (Table 21) is refuted by decide.
Countability beyond the binary (his §2): Welsh, Turkana, Maltese (tripartite: non-countable, collective/singulative, singular/plural) and Dagaare (four classes, including an inverse-marked one) against English's binary cut and Yudja's near-absent cut.
The markedness/coding prediction (his §4.4, after Jakobson and Greenberg): which value of a class's contrast is zero-coded tracks the class's position on the scale — single-reference default for highly individuated classes, multiple-reference default for aggregate classes (the singulative), no contrast at the bottom. Dagaare's inverse number marking is this prediction at work, not a Number value — confirming the canonical inventory's exclusion of UD.Number.Inv.
Animacy refinement (his §4.2): collective/singulative classes ascend the animacy hierarchy (inverse of Smith-Stark plural marking); the per-language collective regions nest (Maltese ⊆ Welsh ⊆ Turkana).

Connections #

Countability classes are not Number values: Welsh collectives take plural agreement while Maltese collectives take singular ([Gri18] §2.1, §2.3), so the unit/aggregate contrast cross-cuts the agreement values — vindicating the value space of Features/Number/Basic.lean.
Each class carries a Number.System (WelshClass.system etc.), so Grimm's classes plug into the implicational universals; this generalizes the two-class CountMassNumberInteraction of Studies/Corbett2000.lean.
English's binary partition is Features.MassCount (english_matches_massCount) — the binary feature becomes the 2-cell instance of the scale, not a primitive.
countable : Bool as a lexical field is refuted twice over: structurally by [Bor05] (see Studies/Borer2005.lean) and scalarly here.

The scale of individuation #

IndividuationType — the scale substance < granular aggregate < collective aggregate < individual ([Gri18] (17)/(19)) — lives in Features/Individuation.lean, shared with [SF21]'s count/mass lexicalization options (Studies/SuttonFilip2021.lean).

The order-preservation thesis #

[Gri18] §3.4: nominal descriptions are partitioned both into individuation types (Π_I, ordered by the scale) and into a language's grammatical countability classes (Π_G, ordered); the thesis is that the classification map is order-preserving (Monotone). The structural consequence — each grammatical class is a contiguous segment of the scale, "no category spans two disconnected segments" — is the Set.OrdConnected-ness of the classification's fibers.

Grimm (2018) — Grammatical Number and the Scale of Individuation #

Core contributions #

Connections #

The scale of individuation #

The order-preservation thesis #

Per-language countability systems ([Gri18] §2, Tables 19–20) #

The impossible system ([Gri18] Table 21) #

Coding and markedness ([Gri18] §3.4 Table 20, §4.4) #

Classes carry number systems #

English's binary cut is MassCount #

Animacy refinement ([Gri18] §4.2) #

English's binary cut is `MassCount` #